Local spectroscopy of the electrically tunable band gap in trilayer graphene

The stacking order in trilayer graphene plays a critical role in determining the existence of an electric field tunable band gap. We present spatially resolved tunneling spectroscopy measurements of dual gated Bernal (ABA) and rhombohedral (ABC) stacked trilayer graphene devices. We demonstrate that while ABA trilayer graphene remains metallic, ABC trilayer graphene exhibits a widely tunable band gap as a function of electric field. However, we find that charged impurities in the underlying substrate cause substantial spatial fluctuations of the gap size. Our work elucidates the microscopic behavior of trilayer graphene and its consequences for macroscopic devices.

Figure 1

Graphene device schematic, Raman spectroscopy, and sample togography. (a) Schematic of the measurement setup showing the STM tip and an optical microscope image of one of the measured samples. Scale bar is 20 $\mu$m. (b) Band structure for ABA and ABC trilayer graphene with no electric field and a moderately sized electric field. To first order, the low energy bands of ABA trilayer graphene are the superposition of the single-layer (roughly linear) and Bernal-stacked bilayer (roughly quadratic) graphene band structures, while the low energy bands of ABC trilayer graphene are roughly cubic. (c) Raman spectroscopy of both stacking orders of trilayer graphene. Left upper inset: map of the FWHM of the 2D peak for an ABA-stacked flake. Right upper inset: map of the FWHM of the 2D peak for an ABC-stacked flake. (d) STM topography image of ABC trilayer graphene showing the triangular lattice. Scale bar is 2 nm. Imaging parameters were sample voltage $-200$ mV and tunneling current 100 pA.

Figure 2

Density of states of ABA and ABC trilayer graphene at varying gate voltage. (a) Experimental dI/dV curves for ABA trilayer graphene taken in regular intervals of back gate voltage between $+$45 V and $-45$ V in steps of $-4.74$ V. Black arrows indicate the location of the bilayerlike conduction band edge. White arrows indicate the location of the bilayerlike valence band edge. (b) Experimental dI/dV curves for ABC trilayer graphene for back gate voltages ranging from $+$45 V and $-45$ V in steps of $-4.74$ V. Black arrows indicate the location of the conduction band van Hove singularity. Black tick marks represent the band gap edges. All curves are the average of 64 measurements taken over a 16 nm by 16 nm range. All curves are offset for visual clarity.

Figure 3

Experimental band gap size in ABC trilayer graphene. Gray circles represent the gap size for the data plotted in Fig. 2. Colored squares represent the gap sizes for eight other spots on the sample. Inset: sample voltage of the valence (red) and conduction (blue) band edges as a function of back gate voltage for the gray circles.

Figure 4

Charge fluctuation and experimental and theoretical band gap size in ABC trilayer graphene as a function of charge density. (a) Experimental dI/dV puddle map for ABC trilayer graphene taken at $V_g=+30$ V. The color scale represents the sample voltage of the van Hove singularity of the conduction band. The scale bar is 10 nm. (b) Experimental gap size for ABC trilayer graphene as a function of charge density. All color conventions are identical to Fig. 3. The black curve is the theoretically expected gap size as a function of charge density.